Robert C. Schmidt

Single-Trial Phase Precession in the Hippocampus

During the crossing of the place field of a pyramidal cell in the rat hippocampus, the firing phase of the cell decreases with respect to the local theta rhythm. This phase precession is usually studied on the basis of data in which many place field traversals are pooled together. Here we study properties of phase precession in single trials. We found that single-trial and pooled-trial phase precession were different with respect to phase-position correlation, phase-time correlation, and phase range. Whereas pooled-trial phase precession may span 360°, the most frequent single-trial phase range was only ∼180°. In pooled trials, the correlation between phase and position (r = −0.58) was stronger than the correlation between phase and time (r = −0.27), whereas in single trials these correlations (r = −0.61 for both) were not significantly different. Next, we demonstrated that phase precession exhibited a large trial-to-trial variability. Overall, only a small fraction of the trial-to-trial variability in measures of phase precession (e.g., slope or offset) could be explained by other single-trial properties (such as running speed or firing rate), whereas the larger part of the variability remains to be explained. Finally, we found that surrogate single trials, created by randomly drawing spikes from the pooled data, are not equivalent to experimental single trials: pooling over trials therefore changes basic measures of phase precession. These findings indicate that single trials may be better suited for encoding temporally structured events than is suggested by the pooled data.

Market share dynamics in a duopoly model with word-of-mouth communication

We analyze dynamic price competition in a homogeneous goods duopoly, where consumers exchange information via word-of-mouth communication. A fraction of consumers, who do not learn any new information, remain locked-in at their previous supplier in each period. We analyze Markov perfect equilibria in which firms use mixed pricing strategies. Market share dynamics are driven by the endogenous price dispersion. Depending on the parameters, we obtain different ‘classes’ of dynamics. When firms are impatient, there is a tendency towards equal market shares. When firms are patient, there are extended intervals of market dominance, interrupted by sudden changes in the leadership position.

ON THE VALUE OF A LARGE CUSTOMER BASE IN MARKETS WITH SWITCHING COSTS

It is usually acknowledged that firms benefit from a large customer base in markets with switching costs. However, Klemperer [1995] argues that this may not be true if an increase in the size of a firms customer base induces fierce price competition, making the firm worse off. This paper shows that such an outcome can be obtained under standard assumptions, such as homogeneous goods and uniformly distributed switching costs. In the model, firms have very limited incentives to fight for market shares, and the notion that switching costs make markets less competitive is stronger than previously shown.

Trial-to-trial variability of phase precession in the hippocampus

Address: 1Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Invalidenstr. 43, 10115 Berlin, Germany, 2Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, 10115 Berlin, Germany, 3Center for Molecular and Behavioral Neurobiology, Rutgers University, 197 University Ave, Newark, New Jersey 07102, USA, 4Department of Biology II, University of Munich, Großhaderner Str. 2, 82152 Planegg-Martinsried, Germany and 5Neuroscience Research Center, Charité, Universitätsmedizin Berlin, Charitéplatz 1, 10117 Berlin, Germany